next up previous
Next: 3.1 Bad conditioning Up: THE ASTEROID IDENTIFICATION PROBLEM Previous: 2.3 Restricted orbit identification

3. Problems with the linear theory

The linear theory for orbit identification provides the most rigorous mathematical setting to solve this problem. A mathematical theorem, however, is not at all a rigorous tool unless all the hypothesis are applicable to the concrete problem to be solved. The hypothesis needed to apply the formalism of Section 2 are the following:

The normal matrices $C_1, C_2$ and $C_0=C_1+C_2$ are invertible and positive-definite.
The map between the space of the residuals $\xi$ and the space of estimated parameters $X$ is in the linear regime, that is the linearized map $\Delta X= -\Gamma\,B^T\xi$ is a good approximation in a region including both orbits.
The observation errors are of a size consistent with the residual normalization adopted.

In this Section we shall discuss the applicability of these three hypothesis to the problem of orbit identification.


Maria Eugenia Sansaturio